The node-reliability polynomial nRelG(p) measures the probability that a connected network remains connected given that each node functions independently with probability p. Computing node-reliability polynomials nRelG(p) exactly is NP-hard. Here we propose efficient approximations. First, we develop an accurate Monte Carlo simulation, which is accelerated by incorporating a Laplace approximation that captures the polynomial’s main behavior. We also introduce three degree-based stochastic approximations (Laplace, arithmetic, and geometric), which leverage the degree distribution to estimate nRelG(p) with low complexity. Beyond approximations, our framework addresses the reliability-based Global Robustness Improvement Problem (k-GRIP) by selecting exactly k links to add to a given graph so as to maximize its node reliability. A Greedy Lowest-Degree Pairing Link Addition (Greedy-LD) Algorithm, is proposed which offers a computationally efficient and practically effective heuristic, particularly suitable for large-scale networks.

Abstract We introduce two new methods for approximating the all‐terminal reliability of undirected graphs. First, we introduce an edge removal process: remove edges at random, one at a time, until the graph becomes disconnected. We show that the expected number of edges thus removed is equal to , where is the number of edges in the graph, and is the average of the all‐terminal reliability polynomial. Based on this process, we propose a Monte‐Carlo algorithm to quickly estimate the graph reliability (whose exact computation is NP‐hard). Moreover, we show that the distribution of the edge removal process can be used to quickly approximate the reliability polynomial. We then propose increasingly accurate asymptotics for graph reliability based solely on degree distributions of the graph. These asymptotics are tested against several real‐world networks and are shown to be accurate for sufficiently dense graphs. While the approach starts to fail for “subway‐like” networks that contain many paths of vertices of degree two, different asymptotics are derived for such networks.

In this paper, we propose closed-form analytic approximations for the number of controllable nodes in sparse communication networks from the aspect of network controllability, considering link-based random attack, targeted attack, as well as random attack under the protection of critical links. We compare our approximations with simulation results on communication networks. Results show that our approximations perform well for all three attack strategies as long as the fraction of removed links is small. Only when the fraction of removed links is large, our approximation for targeted attacks does not fit well with simulation results. Finally, we validate our approximations using 200 communication networks and some synthetic networks. Results show that our approximations perform well in most cases.

The linear relation between Kemeny’s constant, a graph metric directly linked with random walks, and the effective graph resistance in a regular graph has been an incentive to calculate Kemeny’s constant for various networks. In this paper we consider complete bipartite graphs, (generalized) windmill graphs and tree networks with large diameter and give exact expressions of Kemeny’s constant. For non-regular graphs we propose two approximations for Kemeny’s constant by adding to the effective graph resistance term a linear term related to the degree heterogeneity in the graph. These approximations are exact for complete bipartite graphs, but show some discrepancies for generalized windmill and tree graphs. However, we show that a recently obtained upper-bound for Kemeny’s constant in Wang et al. (2017) based on the pseudo inverse Laplacian gives the exact value of Kemeny’s constant for generalized windmill graphs. Finally, we have evaluated Kemeny’s constant, its two approximations and its upper bound, for 243 real-world networks. This evaluation reveals that the upper bound is tight, with average relative error of only 0.73%. In most cases the upper bound clearly outperforms the other two approximations.

The robustness of smart grids is challenged by unpredictable power peaks or temporal demand oscillations that can cause blackouts and increase supply costs. Planning of demand can mitigate these effects and increase robustness. However, the impact on consumers in regards to the discomfort they experience as a result of improving robustness is usually neglected. This paper introduces a decentralized agent-based approach that quantifies and manages the tradeoff between robustness and discomfort under demand planning. Eight selection functions of plans are experimentally evaluated using real data from two operational smart grids. These functions can provide different quality of service levels for demand-side energy self-management that capture both robustness and discomfort criteria.

In First Person Shooter (FPS) games the Round Trip Time (RTT), i.e., the sum of the network delay from client to server and the network delay from server to client, impacts the gamer's performance considerably. Game client software usually has a built-in process to measure this RTT (also referred to as ping time), and therefore gamers do not want to connect to servers with a long ping time. This paper develops a methodology to evaluate the ping time in a scenario where gamers access a common gaming server over an access network, consisting of a link per user that connects this user to a shared aggregation node that in turn is connected to the gaming server via a bottleneck link. First, a model for the traffic the users and the server generate, is proposed based on experimental results of previous papers. It turns out that the characteristics of the (downstream) traffic from server to clients differ substantially from the characteristics of the client-to-server (upstream) traffic. Then, two queuing models are developed (one for the upstream and one for the downstream direction) and combined such that a quantile of the RTT can be calculated given all traffic and network parameters (packet sizes, packet inter-arrival times, link rate, network load, ...). This methodology is subsequently used to assess the (quantile of the) RTT in a typical Digital Subscriber Line (DSL) access scenario. In particular, given the capacity dedicated to gaming traffic on the bottleneck link (between the aggregation node and gaming server), the number of gamers (or equivalently the gaming load the bottleneck link can support) is determined under the restriction that the quantile of the RTT should not exceed a predefined bound. It turns out that this tolerable load is surprisingly low in most circumstances. Finally, it is remarked that this conclusion depends to some extent on the details of the downstream traffic characteristics and that measurements reported in literature do not give conclusive evidence on the exact value of all parameters, such that, although the qualitative conclusion still remains valid, additional experiments could refine the detailed quantitative results.